How Is an Astronaut's Apparent Weight Calculated in Space?

[drewdiddy]

Homework Statement

What is the apparent weight of a 75 kg astronaut 2500 km from the center of the Moon in a space vehicle (a) moving at constant velocity and (b) accelerating towards the moon at 2.3 m/s^2. State direction in each case.

Homework Equations

F=Gm1m2/r^2 and F=mg

The Attempt at a Solution

I solved part a and figure it out. Setting up b is what's giving me troubles. Should this be set up like an elevator/weightless problem or what? I'm uber confused.

 

[drewdiddy]

Disregard.. Figured it out.

 

[baba89]

I would approach this problem by first defining the variables and clarifying any potential assumptions. The apparent weight of a 75 kg astronaut refers to the force that the astronaut experiences due to gravity, which can be calculated using the equation F=mg, where m is the mass of the astronaut and g is the acceleration due to gravity. In this case, m=75 kg. However, since the astronaut is in space and not on the surface of the Moon, the value of g will be different. To calculate g at a distance of 2500 km from the center of the Moon, we can use the formula F=Gm1m2/r^2, where G is the gravitational constant, m1 is the mass of the Moon, and r is the distance from the center of the Moon.

Now, for part a, where the space vehicle is moving at a constant velocity, we can assume that the astronaut is also moving at that velocity, and therefore, there is no acceleration. This means that the acceleration due to gravity, g, will remain constant, and the apparent weight of the astronaut will be the same as it would be on the surface of the Moon. However, the direction of the weight will be different since the astronaut is not standing on the surface of the Moon. It will depend on the orientation of the space vehicle and the position of the astronaut within it.

For part b, where the space vehicle is accelerating towards the Moon at 2.3 m/s^2, we can use Newton's second law, F=ma, to calculate the apparent weight. In this case, the acceleration due to gravity, g, will not remain constant as the space vehicle is accelerating towards the Moon. Therefore, we will need to recalculate g using the formula F=Gm1m2/r^2, where m1 is the mass of the Moon and r is the distance between the space vehicle and the center of the Moon, which will be changing due to the acceleration. The direction of the apparent weight will also change, as it will be in the direction of the acceleration of the space vehicle.

In summary, the apparent weight of the astronaut in both cases will depend on the distance from the center of the Moon, the mass of the Moon, and the acceleration of the space vehicle. The direction of the weight will also depend on the orientation and acceleration of the space vehicle. It is important to carefully define and consider all variables